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Air exchange between an enclosure and its surroundings |
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One of the pleasanter surprises of recent times is that air pollution now comes from inside the house rather than from outside. That means that we have some chance of combatting slow poisoning by tainted air. Museums have a more difficult task because the already dead objects on display have no ability to heal themselves. They are passive absorbers of the corrosive gases that waft past them while we humans have some ability to detoxify our systems, so we are sensitive to concentration of pollutants in the air we breathe, rather than to the absolute accumulation of pollutants on an absorbent surface.
In this article I will first describe air movement on the scale of the individual showcase and then on the scale of the room.
Air in a showcase exchanges with room air at a rate that depends mainly on the construction of the case. Changes of atmospheric pressure and air movement in the room play a lesser role.
As a very general rule the leakage rate of a showcase can be expressed as the air exchange rate in volumes per hour, or day.
Consider an empty case with an exchange rate of one tenth of its volume every hour (which can also be stated as one air change per 10 hours). The air inside is initially completely dry. The case is placed in a room at 100% RH. During the first hour 10% of the air in the case leaks out and is replaced by room air. After mixing, the air in the case has a RH of 10% (0. 1 x 100 RH units from the incoming air plus 0. 9 x 0 RH units from the remaining air). During the next hour 10% of this air leaks out and is replaced. The RH% inside is now 0. 1 x 100 + 0.9 x 10 = 19%, not the expected 20%. After the third hour the RH inside is 0. 1 x 100 + 0. 9 x 19 27%. The rate of change towards 100% is slowing. Theoretically the case will never attain 100% RH, even though the air exchange rate is once every 10 hours. The rate of change of RH is falling in proportion to how close it is to the room value.
Such processes are very common even in everyday life. The rate of the process is at every moment proportional to the remaining difference that is driving it. If one measures the situation at frequent intervals, the calculation moves towards a limiting formula in this way:
Suppose we sample every hour:
After one hour the inside concentration can be formulated case1 =case0 + 0.1 x room - 0.1 x case0. After 2 hours case2 = case1 + 0.1 x room - 0.1 x case1. After 3 hours case3 = case2 + 0.1 x room - 0.1 x case2.
This process is described as exponential and is defined by the equation:
RH in case at time t = 100 x (I - exp(-0.1 x t))
.The exp part of this equation is shorthand for a constant e (= 2.718) raised to the power (-0.1 x t).
This is graphed below.
We are often interested in the concentration to be expected after a certain time has elapsed. Instead of using the air exchange rate, which does not describe directly the concentration after a certain time, we can define the leakage in terms of the time taken for the concentration of water vapour to come half way to the final value. How long does it take the case to reach 50% RH? It takes about 7 hours (vertical line on graph). It will take a further seven hours to reach half way between 50 and 100 = 75% RH, and so on.
The general equation for progress towards equilibrium with the RH of the room air is: concentration at hour t = the room concentration x (I - exp(-k x t)) (1)
k is the leakage rate expressed in case volumes per hour.
If we put the concentration at time t to half the room RH and solve for t, we get the half time to reach a new equilibrium. This turns out to be always 0.693 times the leakage rate expressed in hours for one air change. As a simple rule of thumb:
The half time to equilibrium = 0. 7 x the air exchange rate
The calculation described above applies to any gas leaking into, or out of a case whose materials or contents do not interact with the gas. Water vapour is, however, strongly absorbed by many materials. If the case encloses a piece of paper, initially bone dry, the paper will absorb some of the water vapour that leaks into the case, thus prolonging the time needed to reach 50%RH.
This phenomenon can be deliberately used to stabilise the RH in a leaky case. If the leakage rate is known and the likely RH difference between case and room can be estimated, it is possible to predict the amount of paper, or other moisture buffer, that will be needed to give a defined stability.
Suppose that we want the showcase to survive a two month tropical wet season with the rise in inside RH limited to 25%.
We will first find the corresponding leakage rate. Using equation (1)
25 = 100 x (I - exp(-kx 1440)),
k is the unknown leakage rate that will allow the case to function as specified.
Rearranging:
I - 25/100 = exp(-kx 1440)
ln(0.75) = -k x 1440
k = 2 x 10-4 air changes per hour.
This is 500 times less than the measured leakage rate. We can now add to the case a buffer, such as wood, paper or silica gel, which, in the course of changing its equilibrium RH from 0 to 25%, will absorb 500 times the weight of water vapour in the air in the case at 25% RH. Looking at the matter another way, the buffer is making the case behave as though it were 500 times as big, but with an unaltered air leakage rate in cubic metres per hour.
From the psychrometric chart we find that the moisture content of air at 25C and 25% RH is 0.005 kg/kg. We use the rule of thumb that air at any temperature and RH that is tolerable in a museum has a density of about 1.2 kg per cubic metre. The weight of water vapour in the case is therefore 0.006 kg/M3.
We have to add to the case a weight of paper per cubic metre that will absorb 500 x 0.006 = 3 kg of water, while moving from equilibrium at 0% to 25% RH. From the data sheet for the absorption isotherm for wood, which is similar to paper, we find about 6% water content at 25% RH. We therefore need 100/6 x 3 = 50 kg of wood or paper. If the case is a one metre cube it will need a stack of paper covering the bottom of the case to a depth of about 100 mm.
About one tenth of the case volume is occupied by RH buffer. This is quite practical, and also helps to stabilise the case against knocks, but it is a slight fire hazard. Wood is not to be recommended because it outgasses corrosive chemicals. Silica gel is more expensive, two or three times as good a buffer per kilogram, inert but prone to dust as it absorbs and desorbs water. Improved varieties of silica gel buffer are available and popular among conservators with big budgets.
The ability of the water to diffuse through the buffer material into the air in the case is also an exponential process. It may be necessary to build extra porosity into the mass of buffer to ensure that the water is available during the two months it is needed.
This worked example is quite realistic. A well constructed case with silicone sealing at joints and round the door will have an air exchange rate between 6 and 24 hours. 10% of the case volume allotted to the buffer is quite reasonable. The 100% RH difference with the room is exceptional. More usual is a case at 50% RH that must endure a northern winter with 20% RH in the room for about four months, without falling below 40% RH. If such numbers are put into the equation the resulting buffer requirement is of the same order of magnitude. A well built case needs about 10% by volume of buffer (usingpaper as a standardfor calculation) to survive seasonal extremes of weather.
The rule of thumb stated above is useful because it is rather difficult to measure the leakage rate in order to make a more scientific calculation of the buffer requirement.
The standard method for measuring air exchange rates is to release into the case a slow, known flow of an unusual, inert but detectable gas. The gas mixes with, and flows with the air. The equilibrium concentration depends on the competition between release rate and leakage rate. This equilibrium concentration is measured by placing small open ended tubes which have an absorber at the bottom. The narrowness of the tube ensures that the gas reaches the absorber by diffusion through still air, unaffected by the rate of flow of contaminated air across the opening.
The commonly used tracer gases are fluorine compounds in small glass tubes, leaking at a constant rate through porous plugs. The gas absorbed into the detector tubes is usually analysed by gas chromatography. The process is beyond the technical capacity of most museums. There is a need for a simple analytical system capable of quantitative analysis of a gas inert to all materials found in showcases.
In an empty case, water vapour can be used as a tracer by measuring RH change. In a case with buffer materials already installed the RH record indicates not the air leakage rate but a "RH change rate". This is useful if the purpose of the measurement is to estimate humidity stability of the case, because it avoids all the calculations described above! It does not however indicate how good the case is at preventing entry of dust and pollutants. For this purpose we need an inert tracer gas.
Many museum rooms have an RH which varies with a daily cycle but, when averaged over several weeks is acceptable. Calculation of the resulting variation inside a showcase is quite complicated, requiring computer simulation of the process of leakage and of reaction of the buffer. In practice, reasonably well sealed cases have adequate buffering against daily RH cycles if they have cotton background or baseplate cloth.
I suspect that silica gel is often used in showcases, and transport cases, as a religious offering to appease Ra, the god of rapid change and premature decay (1). Before stuffing silica gel into showcases it is worth calculating roughly the buffer need of the case and the buffer effect of the furnishing and objects in the case. Even better: build the case more airtight.
Air pollutants from the room will diffuse into the showcase in exactly the same way as the water vapour described above. Once in the case, the pollutants will be absorbed quickly, if reactive, so that an exponential calculation of concentration increase will not be valid. The concentration inside the case will remain low. For this reason it is not useful to measure air pollution in cases with furnishing and objects. If the result is low it could be that the objects are efficient absorbers, or that there is no air pollution entering. If the result is high, panic can be tempered by the thought that the objects cannot be reacting very fast! The best way to judge the threat of air pollution is to measure the leakage rate of the case using a non-reactive gas and then assume that the dangerous gases get in at the same rate and then react quickly.
Modern building materials, as well as some ancient ones, outgas a variety of chemicals. Some are known to be harmful to museum objects. Some are also harmful to humans. Only the latter have been investigated rather thoroughly, with standards set to reduce their abundance. Formaldehyde outgassing from wood products is now subject to stringent control but acetic acid, also from wood, is uncontrolled by legislation. It is a rather abundant museum pollutant that is harmless to people but extremely corrosive to lead.
The best defence is not to use wood in showcases, the next best solution is to coat internal surfaces of wooden showcases with aluminium foil. If the objects themselves are of wood and must be exhibited close to lead objects the only solution is to put a pollutant absorber in the case. The absorber must compete efficiently with the object for the pollutant. This means building trays of absorber into the case with holes to allow good circulation of air over the absorber.
1. Ra, the Egyptian god of the sun, was born again each dawn, grew from childhood to maturity at midday, then aged and died at sunset.
This work is licensed under a Creative Commons Attribution-Noncommercial-No Derivative Works 3.0 Unported License.
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